The pump excitation is introduced in our second-quantized electrons through the standard Peierls substitution \(t_\mathrm {h}c^\dagger _{i \sigma } c_{i+1\sigma } \rightarrow t_\mathrm {h} e^{i{A}(t)} c^\dagger _{i \sigma } c_{i+1\sigma }\) , where \({A}(t)\)  is the vector potential projected onto the chain direction. We simulate the pump pulse with an oscillatory Gaussian vector potential \({A}(t)=A_0\, e^{-t^2/2\sigma _\mathrm {pump}^2} \cos (\Omega t)\)  with fixed width \(\sigma _\mathrm {pump} = 3 t_\mathrm {h}^{-1}\) , and variable amplitude \(A_0\)  and frequency \(\Omega \) . The ground state of the EHM is calculated by the parallel Arnoldi method with Paradeisos acceleration [1]}, [2]} and the time evolution is evaluated by the Krylov subspace technique [3]}, [4]}. We adopt a 12-site chain with periodic boundary conditions, zero temperature, and quarter filling throughout this paper, due to its proximity to the triplet-pairing phase [5]}, [6]}.
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